| In this work, a new technique to overcome storage/solution problems is developed and applied to an already proven/robust solution procedure, the Method of Moments. The Method of Moments traditionally has limitations in solving electrically large electromagnetic scattering problems, due to the fact that a discretization of the surface of the object is required. The area of the surface must be discretized into small enough subdomains to obtain sufficient results, small enough meaning about 10 subdomains per wavelength for two-dimensional objects and 200–300 subdomains per square wavelength using triangular patches on three-dimensional objects. In usual practice, the problem has several thousand unknowns for large, complex problems. This requirement quickly becomes expensive in terms of computational resources and may even become impossible to handle. Hence, there is a need to develop alternate schemes to reduce the computational resources, one method being to generate a sparse (or ultimately a diagonal) matrix instead of a full/dense matrix. A new technique, coined the Adaptive Basis Function/Diagonal Matrix Multiplication (ABF/DMM) technique, is presented in this work to accomplish this task.; The development of a new set of adaptive basis functions is presented, which, when used in the regular moment method, automatically generates a diagonal/sparse moment matrix. The central idea in this scheme is to group a number of elementary basis functions into one cluster. Then, appropriate complex weights are attached to these individual basis functions in the cluster so that the integrated field value (i.e. the basis function multiplied by the kernel function and integrated over the basis function domain) produces a null in the field over all the other testing domains. This null translates to zero elements in the moment matrix, thus enabling the generation of a diagonal/sparse system impedance matrix. Obviously, the evaluation of the appropriate weights is the crucial step in this method, which is discussed in a simple procedure. One major advantage of this new method is that only the non-zero elements in the moment matrix are to be generated, which reduces the computer storage requirements substantially. Hence, this diagonal/sparse impedance matrix allows for a more efficient solution.; Furthermore, this method is applied to several conventional electromagnetic scattering problems. These problems include: (1) induced currents on two-dimensional perfect electric conductors from incident transverse-electric and transverse-magnetic plane waves, (2) scattering from arbitrary three-dimensional perfect electric conductors from an incident plane electromagnetic wave, and (3) induced currents on arbitrarily oriented thin wires due to an incident electromagnetic field. In cases (1) and (2), the adaptive basis functions are used to generate a diagonal impedance matrix. For case (3), the adaptive basis functions are used to generate a strictly banded impedance matrix. Several representative examples are presented for each of these cases to illustrate the validity of this new procedure. |
